The coalition of Ms Merkel's conservative Christian Democratic Union, its Bavaria-only sister party, the Christian Social Union and the centre-left Social Democrats have 399 of the 709 seats in parliament.

Ms Merkel will head a much-changed new cabinet, with the governing parties - which are traditional rivals - keen to send signals of renewal after a September election in which all lost significant ground. There are new faces in the most important posts, the finance, foreign, economy and interior ministries.

The same parties have governed for the past four years but putting together the new administration has been unprecedentedly hard work.

Wednesday's parliamentary vote came 171 days after the election, nearly double the previous record. The Social Democrats initially planned to go into opposition after crashing to their worst result since World War II, but Germany's president nudged them into a reluctant about-turn after Ms Merkel's talks with two smaller parties collapsed in November.

Ms Merkel was able to take office only after two-thirds of the Social Democrats' members approved in a ballot the coalition deal clinched last month. At least 35 coalition lawmakers didn't support her Wednesday, though that was in line with results at the beginning of her two previous "grand coalitions" of Germany's biggest parties.

She will have to hold together what is potentially her most fragile coalition yet in what is widely expected to be her last term, while also addressing challenges such as a potential Europe-US trade war and seeking agreement with France and others on the future of a fractious European Union.